Emergent Decoherence Dynamics in Doubly Disordered Spin Networks

Elucidating the emergence of irreversible macroscopic laws from reversible quantum many-body dynamics remains challenging, particularly in disordered media. Here, in a doubly disordered electron-nuclear spin network in nitrogen-doped diamond, we uncover an emergent decoherence law for ^{13}C polarization, M(t)=e^{-sqrt[R_{p}t]}e^{-R_{d}t}, that persists over >500  s and across broad Hamiltonian regimes. We trace the law to two interdependent, electron-mediated channels: direct depolarization by a fluctuating electron bath and an indirect pathway governed by polarization transport within the dilute nuclear network, which is anomalous and subdiffusive. Combining Floquet engineering with all-optical modulation of the electron environment, we demonstrate deterministic control of the channels and the ability to selectively eliminate either one. Disorder, typically viewed as detrimental, here proves protective by generating rare electron-free clusters that trap polarization and dominate late-time decay.